Question

On discovering that her family had a 70% risk of heart attack, Erin took a treadmill test to check her own potential of having a heart attack. The doctors told her that the reliability of the stress test is 67%. What is the probability that Erin will not have a heart attack and the test predicts that she will?

Answer 1

The probability that Erin will not have a heart attack and the test predicts that she will is, 46.5% .

Hint- This a conditional probability problem where Bayes theorem should be applied.

Solution-

Applying Bayes theorem,

`P(No\ heart\ attack\ |\ Correctly\ tested)`

`=(P(Correctly\ tested\ |\ No\ heart\ attack)P(No\ heart\ attack))/(P(Correctly\ tested))`

`P(Correctly\ tested\ |\ No\ heart\ attack)=67\%=0.67`

`P(No\ heart\ attack)=1-P(heart\ attack)=1-0.7=0.3`

`P(Correctly\ tested)=[P(No\ heart\ attack)* P(Correctly\ tested)]+[P(Heart\ attack)* (Incorrectly\ tested)]`

`=[0.3* 0.67]+[0.7* 0.33]=0.432`

Putting the values,

`P(No\ heart\ attack\ |\ Correctly\ tested)=(0.67* 0.3)/(0.432) =0.465`

∴ There is a 46.5% chance that Erin will not have a heart attack even though the test predicts that she will.

Answer 2

A. 0.099

:)

Explanation: